I'm thinking on doing a Kelvin Varley Divider, but I'm having some trouble finding some information. Is there any advantage of doing each stage with a lower resistance, as the one in Conrad Hoffman's Mini Metrology Lab or using resistances of about the same order of magnitude like the IET Labs KVD-700 (check out page 10)? Maybe lower output impedance? Is that a problem, as it depends more on the input resistors? Doing it with with a smaller set of values should be easier to match them.

One more question. In Conrad Hoffman's KVD, he choose to solder the resistors directly to the terminals, instead of using a PCB. Is that because of thermal EMF?

Thank you,Felipe Maimon

[edit] Corrected the links[edit2] Changed the thread title to better match the discussion

The advantages of using higher resistances is that it reduces the errors from switch contact resistance. The divider can compensate for switch contact resistance, but not for the variation in switch contact resistance. So if the variation is 10mOhms and you want to have accuracies in the order of 1 part in 10-7 (like the Fluke), then you want the primary decade to have a total resistance of at least 100K, which is exactly what Fluke do with its eleven 10K resistors in the first decade.

The problem with higher resistances is that you have to measure the output voltage with something, and the higher the resistance, the more minute test currents will affect the output voltage.

The output resistance of a Kelvin-Varley divide varies with the switch positions, but say it can be as high as 100Kohms, then measuring the output with a 10Mohm multimeter will cause an error of 1% which destroys your 0.00001% accuracy. So you have to decide how you are going to use the divider, what accuracy you need and design accordingly.

The rules for building a Kelvin-Varley divider are:

All resistors in a decade have to match closely - you do not need resistors in one decade to match another. So if you get a pile or 10ppm resistors, you can choose the closest set for the first decade, the next closest set for the next decade and so on.

Each lower decade must have resistors of a value greater then one fifth the higher decade resistors. So if your first decade uses 10K resistors, the second decade must use over 2K resistors. There is nothing at all stopping you using 10K resistors for each decade, so you can buy a big pile of 10K resistors, and select them for the most accurate divider.

Each decade needs a parallel resistor across the whole decade divider so that the decades total resistance exactly equals twice the resistor value in the higher decade. So if the first decade uses 10K resistors, then the second decade will have to have a parallel resistor across the whole decade adjusted so that the total resistance is exactly 20K.

The advantage about using lower resistors in the lower decade is it helps lowering the output resistance as much as possible.

So if a 10Mohm multimeter causes an error of 1%, how do you use it? Many high end meters have input resistances much more then 1G for input voltages between +- 20V. Or you can put a fet input low offset amplifier on the output in a inity gain voltage follower configuration and make sure the FET input currents are low enough not to cause a significant error. Or you can use the divider in a traditional way where you use it with a galvanometer on the output, and you adjust either the divider or the voltage that you are measuring so that the galvanometer shows zero current is flowing.

Thank you for the link. Looks like it's very good. I'll read more thoroughly later.

Quote from: amspire

The advantages of using higher resistances is that it reduces the errors from switch contact resistance. The divider can compensate for switch contact resistance, but not for the variation in switch contact resistance. So if the variation is 10mOhms and you want to have accuracies in the order of 1 part in 10-7 (like the Fluke), then you want the primary decade to have a total resistance of at least 100K, which is exactly what Fluke do with its eleven 10K resistors in the first decade.

The problem with higher resistances is that you have to measure the output voltage with something, and the higher the resistance, the more minute test currents will affect the output voltage.

The output resistance of a Kelvin-Varley divide varies with the switch positions, but say it can be as high as 100Kohms, then measuring the output with a 10Mohm multimeter will cause an error of 1% which destroys your 0.00001% accuracy. So you have to decide how you are going to use the divider, what accuracy you need and design accordingly.

So the best way to use the KVD is by buffering it's output with a chopper stabilized amp (OPA735 looks a good candidate), if you intend to read or use its output for anything other than a wheatstone bridge, right?

Quote from: amspire

The rules for building a Kelvin-Varley divider are:

All resistors in a decade have to match closely - you do not need resistors in one decade to match another. So if you get a pile or 10ppm resistors, you can choose the closest set for the first decade, the next closest set for the next decade and so on.[/l][/l][/l][/l]

That's pretty much what I was thinking on doing.

Quote from: amspire

Each lower decade must have resistors of a value greater then one fifth the higher decade resistors. So if your first decade uses 10K resistors, the second decade must use over 2K resistors. There is nothing at all stopping you using 10K resistors for each decade, so you can buy a big pile of 10K resistors, and select them for the most accurate divider.

I didn't thought of that rule, but it makes perfectly sense. 10x the resistors of the second decade has to be greater than 2x the resistor of the first, so you can shunt/trim the second decade to a lower value.

Quote from: amspire

Each decade needs a parallel resistor across the whole decade divider so that the decades total resistance exactly equals twice the resistor value in the higher decade. So if the first decade uses 10K resistors, then the second decade will have to have a parallel resistor across the whole decade adjusted so that the total resistance is exactly 20K.

Thats pretty much in sync with the previous rule.

Quote from: amspire

The advantage about using lower resistors in the lower decade is it helps lowering the output resistance as much as possible.

So if a 10Mohm multimeter causes an error of 1%, how do you use it? Many high end meters have input resistances much more then 1G for input voltages between +- 20V. Or you can put a fet input low offset amplifier on the output in a inity gain voltage follower configuration and make sure the FET input currents are low enough not to cause a significant error. Or you can use the divider in a traditional way where you use it with a galvanometer on the output, and you adjust either the divider or the voltage that you are measuring so that the galvanometer shows zero current is flowing.

Lol. Just noticed I didn't read you first response properly, as you've pretty much answered my first question in this post.

Everything I did was driven by cost and ease of construction. If I had specified good rotary switches the cost would be so high that nobody would build the project. The same thing for getting very stable wire wound or metal foil resistors. Most KVDs are built point to point on the switch terminals, probably to keep leakage at a minimum. If you use a PCB, clean it very well. I didn't want to shunt the decades by much, thus the traditional resistor values for each decade. You can certainly build a lower impedance divider if you want. KVDs are only useful if no current flows in the pickoff lead. Either use a gig input impedance bench meter, a null detector and second voltage source (the traditional way) or the chopper stabilized buffer.

There are some clever alternatives these days. You can set up a bank of simple dividers and sum the results with a chopper stabilized amp. Done that way you can even get away with using analog switches and maintain accuracy.

Building a KVD is really a learning exercise. If you just want a KVD to use, it's easier to pick up a used Julie Research, ESI or Fluke. The Fluke has the advantage of being trimmable, as as said above, the manual is worth the read.

If you just want to adjust or confirm the ranges of a DVM, go for the Hamon divider, as it's far easier to build.

One of the great advantages of a Kelvin-Varley divider is that it is totally passive. If the Fluke 720A is connected to 1100V, you can get any voltage out from 0V to 1100V. If I were adding an output amplifier, I would have it so it could be switched out of circuit, so you are not limited to the voltage ranges that the op-amp can cope with.

If you are after accuracy, you do have to invest in good resistors - the more powerful the better as they will heat up less. The last time I was balancing a bridge-type circuit built on 0.1% 25ppm SMD resistors, just the 10V I had across a 10K 10:1 divider was enough power to see the resistors drift due to heating. In a 10:1 divider one resistor gets 9 times the power of the other resistor, so one resistor heats more then the other. Because of the drift, best accuracy I could get was probably 0.005% even though I had the resolution to adjust within 0.000001%. I would love to have some of the unbelievable Vishay metal foil resistors, but their prices really hurt.

And I thank you for that. Your Mini Metrology Lab is what sparked me on starting this.

Quote from: Conrad Hoffman

If I had specified good rotary switches the cost would be so high that nobody would build the project. The same thing for getting very stable wire wound or metal foil resistors. Most KVDs are built point to point on the switch terminals, probably to keep leakage at a minimum. If you use a PCB, clean it very well. I didn't want to shunt the decades by much, thus the traditional resistor values for each decade. You can certainly build a lower impedance divider if you want. KVDs are only useful if no current flows in the pickoff lead. Either use a gig input impedance bench meter, a null detector and second voltage source (the traditional way) or the chopper stabilized buffer.

I really liked the idea of using headers to switch each decade and I intend on doing just that.

On doing the PCB, although I have soldering experience, I think I would heat each resistance even less with it than soldering directly to the pin headers, so I expect to maintain the resistor values during soldering. My only fear was the thermal EMF because of the copper in the PCB.

As I have a Fluke 8840A, I'll initially use it to read the KVD output. It's spec'd at higher than 10G, so it's enough. I just hope that it's still near its accuracy number, as I bought it from eBay and still havn't sent it for calibration.

Quote from: Conrad Hoffman

There are some clever alternatives these days. You can set up a bank of simple dividers and sum the results with a chopper stabilized amp. Done that way you can even get away with using analog switches and maintain accuracy.

Can you please elaborate a bit further? Do you mean using a summing amplifier, where you set the summing ratios of each divider is set by the resistors in the amplifier? How can you mantain accuracy when using analog switches (I believe you mean the 74HC405X or similar series) when the switch resistance can be as high as 200R and highly non-linear?

Quote from: Conrad Hoffman

Building a KVD is really a learning exercise. If you just want a KVD to use, it's easier to pick up a used Julie Research, ESI or Fluke. The Fluke has the advantage of being trimmable, as as said above, the manual is worth the read.

Unfortunately, even used, they are pricey, and with shipping (when the seller ships!) and taxes to Brasil, it's way beyond my league.

Quote from: Conrad Hoffman

If you just want to adjust or confirm the ranges of a DVM, go for the Hamon divider, as it's far easier to build.

Initially I just want to have a KVD, but I wan't to use it as a precision voltage source by using a voltage reference and a chopper buffer, something like the one Dave just got.

What, other than offset voltage, drift and voltage gain, do you usually watch for when looking for a chopper stabilized amp?

Quote from: amspire

One of the great advantages of a Kelvin-Varley divider is that it is totally passive. If the Fluke 720A is connected to 1100V, you can get any voltage out from 0V to 1100V. If I were adding an output amplifier, I would have it so it could be switched out of circuit, so you are not limited to the voltage ranges that the op-amp can cope with.

I'll add an amplifier, later, because I want to make a precision voltage source. But I'll make it detachable, so I can still use the KVD alone.

Quote from: amspire

If you are after accuracy, you do have to invest in good resistors - the more powerful the better as they will heat up less. The last time I was balancing a bridge-type circuit built on 0.1% 25ppm SMD resistors, just the 10V I had across a 10K 10:1 divider was enough power to see the resistors drift due to heating. In a 10:1 divider one resistor gets 9 times the power of the other resistor, so one resistor heats more then the other. Because of the drift, best accuracy I could get was probably 0.005% even though I had the resolution to adjust within 0.000001%. I would love to have some of the unbelievable Vishay metal foil resistors, but their prices really hurt.

I'm looking for accuracy, but not that much. I'll use through hole resistors, as these have better thermal dissipation. Did you try making the traces and pads wider, so it acts as a heat sink?It's already expensive buying low ppm resistors (~$.6-$1 each), but those metal foil are crazy!

What, other than offset voltage, drift and voltage gain, do you usually watch for when looking for a chopper stabilized amp?

Many of the chopper stabilized opamps have a low frequency response, but that is fine for a DC reference. So you are looking at offset, drift and input current.

Quote

Quote from: amspire

If you are after accuracy, you do have to invest in good resistors - the more powerful the better as they will heat up less. The last time I was balancing a bridge-type circuit built on 0.1% 25ppm SMD resistors, just the 10V I had across a 10K 10:1 divider was enough power to see the resistors drift due to heating. In a 10:1 divider one resistor gets 9 times the power of the other resistor, so one resistor heats more then the other. Because of the drift, best accuracy I could get was probably 0.005% even though I had the resolution to adjust within 0.000001%. I would love to have some of the unbelievable Vishay metal foil resistors, but their prices really hurt.

I'm looking for accuracy, but not that much. I'll use through hole resistors, as these have better thermal dissipation. Did you try making the traces and pads wider, so it acts as a heat sink?It's already expensive buying low ppm resistors (~$.6-$1 each), but those metal foil are crazy!

The stand alone resistors will have a much lower temperature rise then SMD's. Wider traces may have an effect but probably doesn't matter. Work really hard not to have any mechanical stress on the resistors, so bend the legs to match the mounting exactly before you solder. Stress on a component is one of the factors that cn result in a slow long term drift.

What you can also do is in the first decade, use 2 or 3 resistors in series to make up each divider resistor. It gives you more combinations to end up with 10 exactly matched divider resistors, spreads the thermal load, and gives you a higher input voltage level that the divider can take. So if you got 3k3 resistors, the first decade can be 3 in series to make up one divider resistor and all the other decades use one of the 3k3. If you want to save money, you can go to cheaper resistors after the 3rd decade. What I have found is that the more you can match resistors rather then have adjustment pots, the better the final long term stability. If you do have adjustment pots, it is better if it only has to adjust over +/- 0.01% rather then +/- 1%. I haven't looked at the fluke, but I would think its adjustment on the first stage resistors is probably something like +/- 0.0005%

Yes, pots are trouble! When Julie Research did their KVDs, they matched the resistors as best they could (which was very good) but then soldered a short length of resistance wire to one end of each resistor to get the final value. You'll also find that regular metal films will change value when you solder them, so use long leads, heat clips and work fast. Read the old article a good number of times because I think it mentions all sorts of things to watch for. BTW, it was 15 years ago, so I don't remember as much as you might think.

See if you can download the manual for an Analogic 8200 (same as Data Precision 8200) voltage source. That will show you how to use analog switches, but basically if you're feeding a high impedance opamp from a divider, having 200 ohms in series with the input doesn't matter, and whatever pickoff point is connected swamps out the leakage of the other ones. It's all about ratio of impedances. Then, the decade amps are all summed by another amp, using different value summing resistors so each decade has the correct weight in the final answer. The 8200 doesn't actually use decades, but octal, since it's no problem for a processor to display it.

Many of the chopper stabilized opamps have a low frequency response, but that is fine for a DC reference. So you are looking at offset, drift and input current.

That's pretty much what I thought. Thank you.

Quote from: amspire

The stand alone resistors will have a much lower temperature rise then SMD's. Wider traces may have an effect but probably doesn't matter. Work really hard not to have any mechanical stress on the resistors, so bend the legs to match the mounting exactly before you solder. Stress on a component is one of the factors that cn result in a slow long term drift.

What you can also do is in the first decade, use 2 or 3 resistors in series to make up each divider resistor. It gives you more combinations to end up with 10 exactly matched divider resistors, spreads the thermal load, and gives you a higher input voltage level that the divider can take. So if you got 3k3 resistors, the first decade can be 3 in series to make up one divider resistor and all the other decades use one of the 3k3. If you want to save money, you can go to cheaper resistors after the 3rd decade. What I have found is that the more you can match resistors rather then have adjustment pots, the better the final long term stability. If you do have adjustment pots, it is better if it only has to adjust over +/- 0.01% rather then +/- 1%. I haven't looked at the fluke, but I would think its adjustment on the first stage resistors is probably something like +/- 0.0005%

Using multiple resistors is a pretty good idea. That should also help matching sets, as you can combine them anyway you like.

Note taken about the pots. I'll try to match the resistor as best I can and make the adjustments the pots make as small as possible.

The fluke looks like it has lots of pots! Check the attached schematic.

Yes, pots are trouble! When Julie Research did their KVDs, they matched the resistors as best they could (which was very good) but then soldered a short length of resistance wire to one end of each resistor to get the final value. You'll also find that regular metal films will change value when you solder them, so use long leads, heat clips and work fast. Read the old article a good number of times because I think it mentions all sorts of things to watch for. BTW, it was 15 years ago, so I don't remember as much as you might think.

I'm reading the article a lot.

Quote from: Conrad Hoffman

See if you can download the manual for an Analogic 8200 (same as Data Precision 8200) voltage source. That will show you how to use analog switches, but basically if you're feeding a high impedance opamp from a divider, having 200 ohms in series with the input doesn't matter, and whatever pickoff point is connected swamps out the leakage of the other ones. It's all about ratio of impedances. Then, the decade amps are all summed by another amp, using different value summing resistors so each decade has the correct weight in the final answer. The 8200 doesn't actually use decades, but octal, since it's no problem for a processor to display it.

That's one thing google can't find... Or maybe my googlefu is not that good... The only manual I found is an users manual describing the functions. It didn't have a schematic.

I think I got the idea. One amplifier in a follower configuration (gain of 1) for each decade and another for summing everything. But that brings the problem of matching ratios of resistors in the summing amplifier. Maybe the Hamon idea can be used in here...

Can you explain better how the octal thing works? As it's easier to find analog switches in multiples of 2, it should be easier to construct.

Instead of 10 resistors for each decade, use 8 (octal, remember ). Then you just have to work in a octal base. For example, the ratio of 0.3125 is 0o24 in octal (I've put the 0o in front of any octal numbers). Then the first "octal decade" (is there a name for this?) is set at the second tap and the second "octal decade" is set on the fourth tap.

Now it's possible to use an easy to find 8 channel analog multiplexer, like the 4051 or similar, but more decades are needed to match the same resolution. Doing the math, you need (log 10 / log 8 ) = about 1.1073 more decades. And now there is another problem of the summing amplifier needing resistors in ratios of multiples of 8, but some modifications of the hamon divider can do it.

Just had an idea. Instead of lots of different resistors for each deacade in the summing amplifiers, use a ladder in similar fashion to the r-2r ladder. If my math is correct, it should look like the schematic below. Now I just need 3 different resistor values. Vout is followed by a buffer, of course.

The summing method means each decade can be built independently, and matching the relative contribution of each decade is done by adjusting one summing resistor for each decade.

The Hamon divider method can be used for ratios that are the square of numbers - ie 22:1, 32:1, 42:1, etc.

That means you get ratios of 4:1, 9:1. 16:1, 20:1 or voltage dividers that divide by 5, by 10, by 17, by 21.

It is hard to see how you would get a divide by 8 ratio.

A better technique that has been used in lots of older instruments is arrange for each decade to go from 0 to 10 (instead of 9).

Then calibration consists of two major steps. Step One is is you get all the resistors within each decade matched to each other.

Step 2 is you adjust each decade, starting from the second most significant so that "10" is exactly equal to "1" on the range above.

If you are using electronic switches, then to match the ranges, you can switch between the "1" on one range and the 10 on the next lower range at rate of 133Hz (or any frequency that is not a mains harmonic). You will get a square wave out when they do not match, and when you adjust the summing resistor for a match, the amplitude of the squarewave will go to zero. If you built an sensitive AC amplifier, along with a tuned 133Hz bandpass filter to eliminate everything but the 133Hz Ac, and put your multimeter on the output, then you can match the decades with extreme precision without needing anything expensive or precise.

So calibration comes down to matching resistors within a decade, and zeroing an AC value. These are two steps that can be done simply and very accurately without expensive equipment.

In practice, any time you are chasing precision, it is always the detail that you have to be obsessive about. You have to consider all the factors you normally do not have to consider in other designs. If you are using analogue switches you have to look at the switch resistance, the switch-to-switch variations of resistance, the temperature coefficient of the switch resistance, the OFF leakage current through the switch, and the leakage current from the supply rails to both sides of the switch. The currents will probably rise exponentially with temperature, so you have to think of the maximum operating temperature.

The beauty of the totally passive resistive-based dividers is that as long as you start with great resistors and great switches, there is nothing else to go wrong. After a few years, it stabilizes and remain incredibly accurate. Put it in the cupboard, drag it out in 20 years and it will still work perfectly.

Part of the genius of the Kelvin-Varley divider is that the whole divider can be build from the built from one single batch of resistors, all of the same value. If all the resistors have matching temperature coefficients, then errors due to ambient temperature changes cancel out. Hopefully, they will age the same too. In the summing method, you have a very wide range of summing resistors, all that have to stay accurate. Is the 1Mohm resistor temperature characteristics going to match the 1Kohm characteristics? Yes if you were Fluke of 50 years ago, and you make all the resistors from wire of the precisely same composition, and yes if you are HP or Fluke today, and you can make a laser trimmed thick film resistor network, where all the resistors are made from exactly the same deposited film. Probably not if you are a hobbyist getting whatever parts you can find.

Just had an idea. Instead of lots of different resistors for each deacade in the summing amplifiers, use a ladder in similar fashion to the r-2r ladder. If my math is correct, it should look like the schematic below. Now I just need 3 different resistor values. Vout is followed by a buffer, of course.

Lol. This thing is looking more like a very big and complex DAC

I think your maths is a bit off with this one. Top marks for getting the values to work successfully as a tree with each stage having the same impedance as the stage below it. That bit is perfect. Very elegant.

The problem is that each stage contributes 7/8 of the previous stage, and that is not much use at all. There is no reason not to use the R-2R instead. Far more use with far less resistors.

So if the top stage is 1 Volt out, the second stage contributes 7/8V out. The third stage 49/64 volts out. The 4th 73/83 volts out, and so on. It is not that in theory it couldn't work in a very strange way. In practice, it would need about 103 stages to get one part in a million resolution - 206 resistors - with a massive amount of redundancy. All of which have to be very precisely matched. It is just not efficient, or convenient in terms of the weird increments.

Now the R-2R is great for ICs, but for discreets, it is a problem. To get a resolution of 10-6, you need 20 stages which means 40 resistors. All 40 resistors have to match precisely.

In theory, each resistor down the chain requires less accuracy then the one above it, but if you want to calibrate it, it is hard without adjustment to one resistor affecting the previous calibrations you have already done.

Someone may have developed a practical technique for calibrating R-2R networks, and I would love to learn of one.

Analogic seems rather possessive of their schematics, and they don't appear on-line anywhere. I'll give you a verbal description of the heart of the thing, the 20 bit DAC. A buffered LM299 reference feeds a divider consisting of 7 resistors, giving 7 voltages, 8 if you include ground. The pickoff points are low value trimmers so the top six can be tweaked slightly.

The voltages all connect to 7 4051 switches connected in parallel. The output of each switch is buffered with a simple follower. Thus, by addressing the control lines of each 4051, you can select one of 8 voltages on 7 different identical buffered outputs.

The output of each follower feeds a summing amp, with each one being summed through a different value resistor, giving you the fine to coarse steps. The beauty of this is that one master divider chain provides the voltages for all the "digits" of precision, rather than needing a separate divider for each digit. I use the term digit loosely since this is octal, not the usual decades we're used to.

This scheme probably makes sense only if you're controlling things with a uP, but it gives 1 ppm resolution and is quite stable. A full calibration does require a good Fluke or Julie KVD, and the calibration numbers are not "friendly". Full scale is something like 1048575. IMO, the same technique could be done with ten voltages and manual control.

That all makes sense. Every Op-amp follower connects to a 4051 one of 8 multiplexer switch. So if you have a 7V reference, each opamp's output can be 0V, 1V, 2V, 3V, 4V, 5V, 6V or 7V depending on the 4051 binary input. If you are using opamps with a 1uV offset, then they will have negligible contribution to the accuracy. Also in this configuration, the resistance and leakage of the 4051 will have negligible effect, as long as the 0-7V divider chain is made up of fairly low impedance resistors. Perhaps a few hundred ohms per resistor.

So lets say the MSO (Most Signifigant Octal - I made that up ) opamp has a 1K resistor to the summing amp.

The next would have an 8K.

Then 64K, 512K, 4.096M, 32.768M and 262.144M for the LSO opamp output. I am sure I have plenty of those 262.144 Megohm resistors somewhere........

May as well make it a 21 bit DAC - you already have the switches for it.

Whereas the Analogic design used binary for the voltages, this plan would use binary coded decimal. So you could use binary coded thumb wheel switches to dial the voltage manually, with a calibration using the last two multiplexer switches to do "1" and "10" for the calibration.

I have added a concept diagram based in Conrad's idea but organized in decades rather then octal/binary.

The is a cost - 12 x 4051's needed rather then 7, but the gains are that you can control it via thumbwheel decade switches, and it is much easier to calibrate.

I have included 2 decades - 4 more have to be added to make a 6 digit voltage source. Each one will have the resistance from the opamp increasing by 10 from the previous decade.

The 10V resistor chain is powered by a 10V reference. Since I have a positive reference, the final op-amp will put out 0 to -10V. In a final design, there would probably be a switchable polarity, or at least a positive polarity.

I haven't included the wiring to the switches, or the extra wiring for my easy-calibrate idea.

By golly I think you've got it! Could be wrong, but I think you can go quite a lot higher on the values for the divider. Since the switches are buffered there isn't any significant load on it, and because something is always connected the leakage resistance of the switches gets swamped out. Analogic/Data Precision did pick off the voltages through low value trimmers, and that probably compensated for any slight loading errors. It also meant you needed a KVD to calibrate the thing. The fixed design just requires identical resistors, something doable with next to no special equipment. I know they have patents on all or some of the design, but I don't know what's still in force.

It wouldn't be hard to combine the Analogic idea with the idea I mentioned about about making each decade go from 0 to 10.

But you could as well stick with octal, or more precisely, septenary (the base-7 system) and apply the same trick. This would allow you to stay with common analog switches. Make each stage go from 0 to 6, and 7 being the same value as the 1 of the next stage. I would, however, recommend a microcontroller to control the switches and do septenary math. And you have to give up the idea of nice decadal voltage steps.

I believe the Analogic was pure binary. The only octal thing about it was probably that each 4051 did 3 bit of resolution.

If you are going to have a micro managing all the voltages settings, to can stick to pure binary. However since you will want to increment in steps of 1uV or 10 uV, to end up with very odd numbers for the high end ranges. Also you could loose the simple summing calibration method I planned.

Not a problem if you happen to have a 7 1/2 digit multimeter or a Fluke 720a for calibration, but if you don't, calibrating a binary system will be rather difficult.

But there are a lot of options, which is why I called it a "concept diagram".

If we can work out a good design, then for each decade, or octal, a module could be put on a small PCB, that we could then source very cheaply. Then anyone could use it to build a voltage source with a many decades or binary bits that they want. Just keep adding modules and summing them.

There are details to be looked at. My low offset opamps have input currents high enough to cause errors. So more effort needed there.

I think easy calibration is the way to go for the average bear. What I don't know is the magnitude of the error sources that "come out in the wash" when the Analogic unit is trimmed. That trimming might have compensated for switch resistance, leakage and who knows what else. The unit did step in 10 uV steps on the 10V range. IMO, one of the nice things about the way they did it was being able to go a bit over 1 or 10V; It's very common to need that feature. I like the idea of modules for each decade. They could have Samtec or similar pin headers so you'd plug them together, creating a block. Doubt it makes much sense to go beyond 1 ppm, as the resistor and reference requirements get way out of hand, not to mention thermal issues. Analogic did make one horrible mistake. They used quadrature switches on the front panel for each decade, that didn't hold up well. The old units can be really unpredictable when setting the voltage, though whatever they read out on the display is what you get. Sometimes you turn it up and it goes down, sometimes down and it goes up. Contact cleaner only helps for a year or two and then becomes ineffective.